Space-bounded quantum state testing via space-efficient quantum singular value transformation

• URL: http://arxiv.org/abs/2308.05079v2
• Date: Thu, 23 May 2024 10:51:36 GMT
• Title: Space-bounded quantum state testing via space-efficient quantum singular value transformation
• Authors: François Le Gall, Yupan Liu, Qisheng Wang,
• Abstract summary: We present a novel complete characterization for space-bounded quantum computation. We consider settings with one-sided error (unitary coRQL) and two-sided error (BQL) Our results reveal that the space-bounded state testing problems all correspond to the same class.
• Score: 2.647089498084052
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Driven by exploring the power of quantum computation with a limited number of qubits, we present a novel complete characterization for space-bounded quantum computation, which encompasses settings with one-sided error (unitary coRQL) and two-sided error (BQL), approached from a quantum state testing perspective: - The first family of natural complete problems for unitary coRQL, i.e., space-bounded quantum state certification for trace distance and Hilbert-Schmidt distance; - A new family of natural complete problems for BQL, i.e., space-bounded quantum state testing for trace distance, Hilbert-Schmidt distance, and quantum entropy difference. In the space-bounded quantum state testing problem, we consider two logarithmic-qubit quantum circuits (devices) denoted as $Q_0$ and $Q_1$, which prepare quantum states $\rho_0$ and $\rho_1$, respectively, with access to their ``source code''. Our goal is to decide whether $\rho_0$ is $\epsilon_1$-close to or $\epsilon_2$-far from $\rho_1$ with respect to a specified distance-like measure. Interestingly, unlike time-bounded state testing problems, our results reveal that the space-bounded state testing problems all correspond to the same class. Moreover, our algorithms on the trace distance inspire an algorithmic Holevo-Helstrom measurement, implying QSZK is in QIP(2) with a quantum linear-space honest prover. Our results primarily build upon a space-efficient variant of the quantum singular value transformation (QSVT) introduced by Gily\'en, Su, Low, and Wiebe (STOC 2019), which is of independent interest. Our technique provides a unified approach for designing space-bounded quantum algorithms. Specifically, we show that implementing QSVT for any bounded polynomial that approximates a piecewise-smooth function incurs only a constant overhead in terms of the space required for special forms of the projected unitary encoding.

Related papers

• Extending Quantum Perceptrons: Rydberg Devices, Multi-Class Classification, and Error Tolerance [67.77677387243135]
  Quantum Neuromorphic Computing (QNC) merges quantum computation with neural computation to create scalable, noise-resilient algorithms for quantum machine learning (QML) At the core of QNC is the quantum perceptron (QP), which leverages the analog dynamics of interacting qubits to enable universal quantum computation.
  arXiv  Detail & Related papers  (2024-11-13T23:56:20Z)
• Quantum Wasserstein Compilation: Unitary Compilation using the Quantum Earth Mover's Distance [2.502222151305252]
  We present a quantum Wasserstein compilation (QWC) cost function based on the quantum Wasserstein distance of order 1. An estimation method based on measurements of local Pauli-observable is utilized in a generative adversarial network to learn a given quantum circuit.
  arXiv  Detail & Related papers  (2024-09-09T17:46:40Z)
• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• Quantum Signal Processing with the one-dimensional quantum Ising model [0.0]
  Quantum Signal Processing (QSP) has emerged as a promising framework to manipulate and determine properties of quantum systems. We provide examples and applications of our approach in diverse fields ranging from space-time dual quantum circuits and quantum simulation, to quantum control.
  arXiv  Detail & Related papers  (2023-09-08T18:01:37Z)
• Quantum process tomography of continuous-variable gates using coherent states [49.299443295581064]
  We demonstrate the use of coherent-state quantum process tomography (csQPT) for a bosonic-mode superconducting circuit. We show results for this method by characterizing a logical quantum gate constructed using displacement and SNAP operations on an encoded qubit.
  arXiv  Detail & Related papers  (2023-03-02T18:08:08Z)
• Fast Quantum Algorithms for Trace Distance Estimation [8.646488471216262]
  We propose efficient quantum algorithms for estimating the trace distance within additive error $varepsilon$ between mixed quantum states of rank $r$. We show that the decision version of low-rank trace distance estimation is $mathsfBQP$-complete.
  arXiv  Detail & Related papers  (2023-01-17T10:16:14Z)
• Implementing quantum walks with a single qubit [7.136104608099681]
  We propose a novel method to implement discrete-time quantum walks (DTQWs) using only a single qubit. We experimentally implement one-particle and two-particle DTQWs with seven steps using single photons.
  arXiv  Detail & Related papers  (2022-06-08T02:04:44Z)
• Multi-state Swap Test Algorithm [2.709321785404766]
  Estimating the overlap between two states is an important task with several applications in quantum information. We design a quantum circuit to measure overlaps of multiple quantum states.
  arXiv  Detail & Related papers  (2022-05-15T03:31:57Z)
• Efficient Bipartite Entanglement Detection Scheme with a Quantum Adversarial Solver [89.80359585967642]
  Proposal reformulates the bipartite entanglement detection as a two-player zero-sum game completed by parameterized quantum circuits. We experimentally implement our protocol on a linear optical network and exhibit its effectiveness to accomplish the bipartite entanglement detection for 5-qubit quantum pure states and 2-qubit quantum mixed states.
  arXiv  Detail & Related papers  (2022-03-15T09:46:45Z)
• Depth-efficient proofs of quantumness [77.34726150561087]
  A proof of quantumness is a type of challenge-response protocol in which a classical verifier can efficiently certify quantum advantage of an untrusted prover. In this paper, we give two proof of quantumness constructions in which the prover need only perform constant-depth quantum circuits.
  arXiv  Detail & Related papers  (2021-07-05T17:45:41Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.